Mrs May will on Tuesday address the UN and defend the Brexit vote, saying that the British people did not back Leave because they want to "turn inwards or walk away".

She will also warn world leaders that the referendum shows that voters want "a politics that is more in touch with their concerns".

Jean-Claude Juncker, European Commission president, kisses Robert Fico, Slovakian prime minister, at the end of the European Union summit in BratislavaCredit:
Reuters

Robert Fico, Slovakia's prime minister, on Monday said that member states intend to make it "very difficult for the UK" and said Britain is "bluffing" when it says it can get a good Brexit deal.

However, Mrs May dismissed those comments and said the 27 other EU members will sign up to "the deal that's right for the UK".

Addressing the warnings made by EU leaders and asked whether it is a sign that they will refuse to do a deal with Britain, Mrs May said: "The 27 will sign up to a deal with us.

"We will be negotiating with them and we will be ambitious in what we want to see for the United Kingdom.

"It's right for us to do that. But I think a good deal for the UK can also be a good deal for the other member states because I believe in good trading relations and I want the UK to be a global leader in free trade."

May: There'll be no second referendum on Brexit

02:47

The Prime Minister added: "I had very constructive meetings with [Mr Fico] when I was doing my visits earlier in the summer.

"We're going to be in a negotiation with the 27 members of the European Union about the relationship we will have with them when we leave the EU.

"I've said what I want to see is the deal that's right for the UK. I think that will also be a deal that's good for the member states of the European Union.

"This is not just about us - it's actually about relationships and trading within that European arena. So we will go into these negotiations and we will be ambitious for the UK."

May: 'I won't trigger Article 50 until we have a UK approach and objectives'

00:17

Mrs May on Monday night met some of America's most powerful business leaders amid concerns that they could be preparing to move their European bases out of the UK in the wake of the Brexit vote.

The Prime Minister, attended a reception with executives from companies including IBM, Morgan Stanley, Goldman Sachs, Black Rock and Amazon.

Theresa May speaks to American business leaders, accompanied by Antonia Romeo, the British Consul General, in New YorkCredit:
PA

Speaking ahead of the meeting, she said that she would tell them that she wants to hear their concerns over the Brexit vote.

American executives want assurances that the rights of their employees based in Britain will be protected once the UK leaves the EU.

Theresa May is greeted by Ban Ki-moon, Secretary-General of the United Nations, at the UN headquarters in New YorkCredit:
Craig Ruttle/AP Photo

Mrs May said: "What I'll be talking about with both American and British business leaders is about how we can encourage that trade and investment between the two countries.

"Remember that there's something like a million people in the UK wake up each morning and then go to work for an American company in the UK.

"I will be talking to them and hearing from them what their emphasis is in terms of the issues they want us to address."

Speaking in Dubai on Monday, Dr Fox backed Mrs May's position that it is in the interests of the EU to do a good deal with Britain.

He said: "To all those who have doubts about Britain’s ability to achieve economic success outside the European Union let me just give you two facts.

"First, if we take the top 10 markets where the UK has a trade surplus only one of them, Ireland, is in the EU.

"And if we look at the 10 markets with which the UK has a trade deficit, seven out of the 10 are in the EU. It is, therefore, very much in the interests of other EU states that Britain and they makes a success of Brexit and our new relationship."